As is known, the tumoral masses present as clear thickenings with linear dimensions ranging from 3 mm to 20–30 mm, have edges that are fuzzy and vary in type and degree of definition. This type of lesions can vary considerably in optical density, from radiolucent cases (appearing dark in mammography), associated generally with benign lesions, to dense lesions with marked radio-opacity, which are frequently malignant. The masses can be distinguished according to shape, position, size, characteristics at the edge, attenuation of the x-rays (index of density), and effects on the surrounding tissue.
In addition, various combinations of shape and edge may be encountered in practice. The type of combination can provide indications on the malignity of the disease. For example, the spiculated lesions, made up of a radio-opaque central nucleus from which there irradiate linear structures known as spiculae, are considered the most typical manifestation of malignant lesions. In spiculated masses, the dense central nucleus corresponds histologically to the tumoral tissue, whilst the spiculae represent the fibrous reaction of the stroma. The latter is the response of the host organism to onset of the tumour. By “architectural distortion” is meant an area where the normal architecture of the breast is distorted, but no definite tumoral mass is visible. In these cases the radiologist marks the presence of a centre of distortion. Also the tissue asymmetries between the right breast and the left breast may be considered pathological and classified as masses.
The visual manifestation in the mammogram of the shape and edge of a lesion does not only depend upon the physical properties of the lesion, but is also affected by the technique of acquisition of the image and above all by the projection considered. A mass may appear round or oval according to the projection, and its edge may be obscured in a particular projection because superimposed on the lesion (in that perspective) are other structures that are normal in the architecture of the breast. This leads to the need, in some cases, to carry out other mammograms in targeted projections which will enable the real lesions to be distinguished from mere tissue folds or effects of superimposition. From what has been said, it is difficult to identify morphological, directional or structural quantities of the mammographic image that can characterize the lesions sought at any scale and any modalities of occurrence. For this reason, many of the algorithms for detecting masses so far developed have concentrated on the detection of just one type of mass or on the detection of masses at a particular scale of search.
In addition, the algorithms up to now used necessitated information on the characteristics of the mass so that the system could learn so as to be able to locate a mass having those characteristics. Consequently, this information on the masses had to be entered into the system by a skilled operator, with a considerable expenditure in terms of time and at the expense of a loss in the degree of precision with which the critical masses were located.
In order to develop a general and effective technique of detection of lesions presenting different characteristics, with the present invention a new approach to the problem of detecting masses has been adopted.
Considering the complexity of the class of objects to be detected, considering that said objects frequently present characteristics that are very similar to the environment in which they are found, and considering the objective difficulty of modelling this class of objects with few measurable quantities, in the approach proposed herein no modelling has been sought. A classifier has thus been trained to recognize a lesion, using basically the original image or a more efficient representation of the original image, with an information content greater than the information content that would be available if a system of recognition based simply upon the levels of grey were to be used.
According to a preferred embodiment, the choice has been made to use, as a representation of the information to be supplied to the classifier, the coefficients of the wavelet representation in the overcomplete form, said coefficients regarding each portion of image that is to be classified. It is likewise possible to use other types of representation, such as, for instance, the levels of grey of the original image. In the wavelet representation, the structural and morphological characteristics of the image are encoded in a more efficient form from the point of view of the information content. The multiresolution analysis proper to the wavelet transform enables highlighting of the structural properties of the image at different scales of resolution.
In addition, the classification of portions of mammographic image, in a representation with high information content, involves the use of a classifier that is able to act on spaces with thousands of dimensions. An effective classification in said spaces has become possible only recently with the development of the trainable classifiers referred to as Support-Vector Machines (SVMs). The learning strategy that SVMs implement remains efficient also in sparse spaces, so enabling a good generalization even after a training step with a number of examples considerably smaller than the dimensions of the classification space, unlike what occurs for other classic algorithms (MLPs, RBF networks). An SVM may achieve a good classification result, in terms of generalization, if at least one of the following conditions is satisfied:
the expected value of the compression of information of the data is high, i.e., few support vectors englobe the structural information on the classes to be learnt;
the hyperplane that separates the two classes is the one that maximizes the distance between the classes themselves, i.e., the classes are well separated within the space of the characteristics;
the dimensions of the input space are few as compared to the number of examples presented.
Furthermore, SVMs perform a sort of automatic check on the information carried by the various characteristics, so enabling a selection thereof.
This is done in two ways:
(1)—only some of the vectors of the two classes determine the decision function, said vectors being referred to as support vectors; in this way, the SVM selects that part of the training vectors which, in the chosen space of the characteristics, carry all the information useful for defining the classes; for the SVM it is not important to know fully how the learning data are distributed in the space of the characteristics; what is important is the behaviour at the edges of the distribution in said space;
(2)—the decision function is the hyperplane of maximum margin, defined by the pair w, b where w is the vector normal to the hyperplane, a linear combination of the support vectors; the said vector w has its larger components along the directions where the data are more separated; i.e., it is directionally more aligned to the base vectors of the space for which the data are more separated; moreover, adding a dimension for which the learning data are totally superimposed, will not vary the hyperplane of separation chosen by the SVM.
Given the ability of the SVM to check multidimensional spaces, at the same time maintaining a good generalization capacity, there has emerged the possibility of eliminating or limiting the step of extraction of the characteristics for a classification task. The automatic search approach adopted by the present invention presents a further advantage, as compared to the methods currently in use, in regard to the fact that the system automatically adapts to the type of images that it has to analyse (x-rays, mammograms, tomograms, NMR scans, etc.), irrespective of the type of machinery used to acquire the image and the conditions of acquisition.